{
  "release": "0.4.0",
  "measured_clock": {
    "source": "NIST Handbook of Basic Atomic Spectroscopic Data, Strong Lines of Hydrogen",
    "centroid_wavelength_nm": 121.56700400000001,
    "energy_gap_eV": 10.198836390933865,
    "period_s": 4.055038769521013e-16
  },
  "thermal_equilibrium_two_level_truncation": {
    "300.0": {
      "bounded_two_level_probabilities_1s_2pz": [
        1.0,
        4.6461098152662925e-172
      ],
      "excited_to_ground_ratio": 4.6461098152662925e-172,
      "maximum_density_matrix_change": 6.32840418327516e-188,
      "coherence_magnitude": 0.0,
      "phase_direction": "undefined because the thermal density matrix has zero 1s-2p_z coherence"
    },
    "10000.0": {
      "bounded_two_level_probabilities_1s_2pz": [
        0.999992755481299,
        7.244518701041972e-06
      ],
      "excited_to_ground_ratio": 7.244571184473399e-06,
      "maximum_density_matrix_change": 9.551031299804915e-22,
      "coherence_magnitude": 0.0,
      "phase_direction": "undefined because the thermal density matrix has zero 1s-2p_z coherence"
    },
    "-10000.0": {
      "bounded_two_level_probabilities_1s_2pz": [
        7.244518701041972e-06,
        0.999992755481299
      ],
      "excited_to_ground_ratio": 138034.39493329916,
      "maximum_density_matrix_change": 1.4712249436314074e-16,
      "coherence_magnitude": 0.0,
      "phase_direction": "undefined because the thermal density matrix has zero 1s-2p_z coherence"
    }
  },
  "coherent_control": {
    "phase_slope_rad_per_s": 1.5494760134985744e+16,
    "expected_magnitude_rad_per_s": 1.5494760134985748e+16,
    "time_reversed_phase_slope_rad_per_s": -1.5494760134985744e+16,
    "temperature_parameter_in_unitary": false
  },
  "written_result": "For rho_beta=exp(-beta H)/Z, [rho_beta,H]=0, so unitary evolution leaves rho_beta stationary. Negative beta in a bounded model reverses population ordering, not the sign of H or time.",
  "boundaries": [
    "The negative-temperature row is meaningful only for the declared bounded two-level truncation; unbounded atomic energy including the continuum does not admit a canonical negative-temperature equilibrium.",
    "Positive temperature has no finite maximum endpoint; beta approaches zero as T approaches positive infinity.",
    "Freezing and melting times depend on heat transfer, heat capacity, and latent heat. They do not by themselves identify microscopic rotation direction.",
    "No measured 3D density or new physical dimension is inferred."
  ]
}